Population dynamics of mutualism and intraspecific density dependence: How θ-logistic density dependence affects mutualistic positive feedback

Abstract

Mutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competition and leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growth is strongly grounded in the behavior of a single model. This model-the Lotka-Volterra competition model with a sign change to generate mutualism rather than competition between species-assumes logistic growth of each species plus a linear interaction term to represent the mutualism. While it is commonly held that the linear interaction term is to blame for the model's unrealistic behavior, we show here that a linear mutualism added to a θ-logistic model of population growth can prevent unbounded growth. We find that when density dependence is decelerating, the benefit of mutualism at equilibrium is greater than when density dependence is accelerating. Although there is a greater benefit, however, decelerating density dependence tends to destabilize populations whereas accelerating density dependence is always stable. We interpret these findings tentatively, but with promise for the understanding of the population ecology of mutualism by generating several predictions relating growth rates of mutualist populations and the strength of mutualistic interaction.

Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

“…Via accurate data analysis, they proposed the following nonlinear competition model with two-species: 2) in which θ 1 , θ 2 represent the nonlinear density restrictions. As pointed out in [6][7][8] that the nonlinear density restrictions model can match well the experimental data on drosophila melanogasters when θ i was far less than 1. From then, Gilpin-Ayala ecosystems have been investigated extensively (see, e.g.…”

Existence and Local Stability of Stationary Solutions for Nonlinear Gilpin Ayala Competition Model with Dirichlet Boundary Value

“…As pointed out in [6][7][8][9], As pointed out in [6][7][8][9], when the parameter θ i is much less than 1, the nonlinear density constrained model can well simulate the population ecology of Drosophila melanogaster. So I assume θ i ∈ (0, 1), and (H1) For each i ∈ {1, 2}, there are positive numbers…”

“…where θ 1 , θ 2 represents the nonlinear density constraint parameter. As pointed out in [6][7][8][9], when the parameter θ i is much less than 1, the nonlinear density constrained model can well simulate the population ecology of Drosophila melanogaster, and the diffusion type Gilpin Ayala competition model under Neumann boundary value condition has also been studied by scholars:…”

Synthetic Mutualism and the Intervention Dilemma

“…Beside the mutual support of two interactors via production of mutually beneficial metabolites, the system also requires an ecological niche. If population densities of mutualistic partners are inadequate, mutualism is hard to sustain [16,83]. This problem highlights the necessity of a physical structure akin to a “warm little pond” for concentrating primary mutualists [84].…”